The Experts below are selected from a list of 132408 Experts worldwide ranked by ideXlab platform
R. M. Lark - One of the best experts on this subject based on the ideXlab platform.
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estimating variograms of soil properties by the Method of Moments and maximum likelihood
European Journal of Soil Science, 2000Co-Authors: R. M. LarkAbstract:Summary Variograms of soil properties are usually obtained by estimating the variogram for distinct lag classes by the Method-of-Moments and fitting an appropriate model to the estimates. An alternative is to fit a model by maximum likelihood to data on the assumption that they are a realization of a multivariate Gaussian process. This paper compares the two using both simulation and real data. The Method-of-Moments and maximum likelihood were used to estimate the variograms of data simulated from stationary Gaussian processes. In one example, where the simulated field was sampled at different intensities, maximum likelihood estimation was consistently more efficient than the Method-ofMoments, but this result was not general and the relative performance of the Methods depends on the form of the variogram. Where the nugget variance was relatively small and the correlation range of the data was large the Method-of-Moments was at an advantage and likewise in the presence of data from a contaminating distribution. When fields were simulated with positive skew this affected the results of both the Method-of-Moments and maximum likelihood. The two Methods were used to estimate variograms from actual metal concentrations in topsoil in the Swiss Jura, and the variograms were used for kriging. Both estimators were susceptible to sampling problems which resulted in over- or underestimation of the variance of three of the metals by kriging. For four other metals the results for kriging using the variogram obtained by maximum likelihood were consistently closer to the theoretical expectation than the results for kriging with the variogram obtained by the Method-of-Moments, although the differences between the results using the two approaches were not significantly different from each other or from expectation. Soil scientists should use both procedures in their analysis and compare the results.
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Estimating variograms of soil properties by the Method‐of‐Moments and maximum likelihood
European Journal of Soil Science, 2000Co-Authors: R. M. LarkAbstract:Summary Variograms of soil properties are usually obtained by estimating the variogram for distinct lag classes by the Method-of-Moments and fitting an appropriate model to the estimates. An alternative is to fit a model by maximum likelihood to data on the assumption that they are a realization of a multivariate Gaussian process. This paper compares the two using both simulation and real data. The Method-of-Moments and maximum likelihood were used to estimate the variograms of data simulated from stationary Gaussian processes. In one example, where the simulated field was sampled at different intensities, maximum likelihood estimation was consistently more efficient than the Method-ofMoments, but this result was not general and the relative performance of the Methods depends on the form of the variogram. Where the nugget variance was relatively small and the correlation range of the data was large the Method-of-Moments was at an advantage and likewise in the presence of data from a contaminating distribution. When fields were simulated with positive skew this affected the results of both the Method-of-Moments and maximum likelihood. The two Methods were used to estimate variograms from actual metal concentrations in topsoil in the Swiss Jura, and the variograms were used for kriging. Both estimators were susceptible to sampling problems which resulted in over- or underestimation of the variance of three of the metals by kriging. For four other metals the results for kriging using the variogram obtained by maximum likelihood were consistently closer to the theoretical expectation than the results for kriging with the variogram obtained by the Method-of-Moments, although the differences between the results using the two approaches were not significantly different from each other or from expectation. Soil scientists should use both procedures in their analysis and compare the results.
Michael Frenklach - One of the best experts on this subject based on the ideXlab platform.
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Method of Moments with interpolative closure
Chemical Engineering Science, 2002Co-Authors: Michael FrenklachAbstract:Abstract The article summarizes the principal details of a Method of Moments with interpolative closure. This is a mathematically rigorous yet numerically economical approach to particle dynamics, describing time evolution of a particle ensemble undergoing simultaneous nucleation, coagulation, and surface growth. The Method was introduced some time ago and since then has undergone further development as well as extensive testing in reactive flow simulations of practical systems. These results, scattered over quite diverse literature, are presented here in a unified form, focussing on logical development rather than on chronological order. In addition, the validity of the numerical approach is addressed on rigorous mathematical grounds. Also discussed are Method shortcomings along with possible directions to their resolution.
Robert Mcgraw - One of the best experts on this subject based on the ideXlab platform.
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description of aerosol dynamics by the quadrature Method of Moments
Aerosol Science and Technology, 1997Co-Authors: Robert McgrawAbstract:The Method of Moments (MOM) may be used to determine the evolution of the lower-order Moments of an unknown aerosol distribution. Previous applications of the Method have been limited by the requirement that the equations governing the evolution of the lower-order Moments be in closed form. Here a new approach, the quadrature Method of Moments (QMOM), is described. The dynamical equations for moment evolution are replaced by a quadrature-based approximate set that satisfies closure under a much broader range of conditions without requiring that the size distribution or growth law maintain any special mathematical form. The conventional MOM is recovered as a special case of the QMOM under those conditions, e.g., free-molecular growth, for which conventional closure is satisfied. The QMOM is illustrated for the growth of sulfuric acid-water aerosols and simulations of diffusion-controlled cloud droplet growth are presented.
Laszlo Matyas - One of the best experts on this subject based on the ideXlab platform.
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generalized Method of Moments estimation
Journal of the American Statistical Association, 1999Co-Authors: Laszlo MatyasAbstract:The generalized Method of Moments (GMM) estimation has emerged as providing a ready to use, flexible tool of application to a large number of econometric and economic models by relying on mild, plausible assumptions. The principal objective of this volume is to offer a complete presentation of the theory of GMM estimation as well as insights into the use of these Methods in empirical studies. It is also designed to serve as a unified framework for teaching estimation theory in econometrics. Contributors to the volume include well-known authorities in the field based in North America, the UK/Europe, and Australia. The work is likely to become a standard reference for graduate students and professionals in economics, statistics, financial modeling, and applied mathematics.
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Generalized Method of Moments Estimation - Generalized Method of Moments estimation
1999Co-Authors: Laszlo MatyasAbstract:The generalized Method of Moments (GMM) estimation has emerged as providing a ready to use, flexible tool of application to a large number of econometric and economic models by relying on mild, plausible assumptions. The principal objective of this volume is to offer a complete presentation of the theory of GMM estimation as well as insights into the use of these Methods in empirical studies. It is also designed to serve as a unified framework for teaching estimation theory in econometrics. Contributors to the volume include well-known authorities in the field based in North America, the UK/Europe, and Australia. The work is likely to become a standard reference for graduate students and professionals in economics, statistics, financial modeling, and applied mathematics.
George Tauchen - One of the best experts on this subject based on the ideXlab platform.
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Efficient Method of Moments
2002Co-Authors: A. Gallant, George TauchenAbstract:We describe a computationally intensive Methodology for the estimation and analysis of partially observable nonlinear systems. An example from epidemiology is the SEIR model, which is a system of differential equations with random coefficients that describe a population in terms of four state variables: those susceptible to disease, those exposed to it, those infected by it, and those recovered from it. Only those infected by the disease are known to public health officials. An example from finance is the continuous-time stochastic volatility model, which is a system of stochastic differential equations that describes a security's price and instantaneous variance. Only the security's price can be observed directly. System parameters are estimated by a variant of simulated Method of Moments known as efficient Method of Moments (EMM). The idea is to match Moments implied by the system to Moments implied by the transition density for observables. System analysis is accomplished by reprojection. Reprojection is carried out by projecting a long simulation from the estimated system onto an appropriate representation of a relationship of interest. A general purpose representation is a Hermite expansion of the conditional density of state variables given observables. A reprojection density thus obtained embodies all constraints implied by the nonlinear system and is analytically convenient. As an instance, nonlinear filtering can be accomplished by computing the conditional mean of the reprojection density and evaluating it at observed values from the data. Ideas are illustrated by using the Methodology to assess the dynamics of a stochastic volatility model for daily Microsoft closing prices.
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The relative efficiency of Method of Moments estimators
Journal of Econometrics, 1999Co-Authors: A. Ronald Gallant, George TauchenAbstract:Abstract The asymptotic relative efficiency of efficient Method of Moments when implemented with a seminonparametric auxiliary model is compared to that of conventional Method of Moments when implemented with polynomial moment functions. Because the expectations required by these estimators can be computed by simulation, these two Methods are commonly used to estimate the parameters of nonlinear latent variables models. The comparison is for the models in the Marron–Wand test suite, a scale mixture of normals, and the second largest order statistic of the lognormal distribution. The latter models are representative of financial market data and auction data, respectively, which are the two most common applications of simulation estimators. Efficient Method of Moments dominates conventional Method of Moments over these models.
